3B · Chapter 8 · exam
Chapter practice examination
Original untimed practice examination. Not a secure or official placement test.
Original untimed practice examination. Not a secure or official placement test. Solutions are available as revealable feedback and in a separate complete answer key. No answer submissions or accounts are required.
Assessment · 24 questions
Questions
Show your thinking; use diagrams when they help. Do not open solutions during your first attempt.
- A1
A student answers the following question with “9”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: 56 counters are shared equally into 7 groups. How many counters are in each group? (3 points)
Reveal explanation
Answer: 8
The suggested answer is not correct. Use inverse multiplication: 7 × 8 = 56; therefore 56 ÷ 7 = 8.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
7 rows of 8 dots = 56 dots. - A2
Find 6 groups of 4. Can you use 5 groups plus one more? (2 points)
Reveal explanation
Answer: 24
6 groups of 4 make 6 × 4 = 24. Or find 5 × 4 and add 4.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
6 rows of 4 dots = 24 dots. - A3
Find 8 groups of 9. Can you use 7 groups plus one more? (2 points)
Reveal explanation
Answer: 72
8 groups of 9 make 8 × 9 = 72. Or find 7 × 9 and add 9.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
8 rows of 9 dots = 72 dots. - A4
Explain how splitting 6 equal groups of 7 helps you find their total. (2 points)
Reveal explanation
Answer: 42
6 groups of 7 make 6 × 7 = 42. Or find 5 × 7 and add 7.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
6 rows of 7 dots = 42 dots. - A5
A student answers the following question with “49”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Compute 6 × 8. Explain a strategy using a known fact. (3 points)
Reveal explanation
Answer: 48
The suggested answer is not correct. 6 groups of 8 make 6 × 8 = 48. Or find 5 × 8 and add 8.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
6 rows of 8 dots = 48 dots. - A6
Each tray holds 6 counters. How many full trays are required to arrange 42 counters? (2 points)
Reveal explanation
Answer: 7
Find how many groups of 6 fit into 42: 42 ÷ 6 = 7.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
6 rows of 7 dots = 42 dots. - A7
Compute 9 × 8. Explain a strategy using a known fact. (2 points)
Reveal explanation
Answer: 72
9 groups of 8 make 9 × 8 = 72. Or find 8 × 8 and add 8.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
9 rows of 8 dots = 72 dots. - A8
Compute 8 × 8. Explain a strategy using a known fact. (2 points)
Reveal explanation
Answer: 64
8 groups of 8 make 8 × 8 = 64. Or find 7 × 8 and add 8.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
8 rows of 8 dots = 64 dots. - A9
A student answers the following question with “57”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: There are 7 equal trays with 8 counters on each tray. How many counters are there? (3 points)
Reveal explanation
Answer: 56
The suggested answer is not correct. 7 groups of 8 make 7 × 8 = 56. Or find 6 × 8 and add 8.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
7 rows of 8 dots = 56 dots. - A10
Each tray holds 8 counters. How many full trays are required to arrange 40 counters? (2 points)
Reveal explanation
Answer: 5
Find how many groups of 8 fit into 40: 40 ÷ 8 = 5.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
8 rows of 5 dots = 40 dots. - A11
There are 9 equal trays with 10 counters on each tray. How many counters are there? (2 points)
Reveal explanation
Answer: 90
9 groups of 10 make 9 × 10 = 90. Or find 8 × 10 and add 10.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
9 rows of 10 dots = 90 dots. - A12
There are 8 equal trays with 5 counters on each tray. How many counters are there? (2 points)
Reveal explanation
Answer: 40
8 groups of 5 make 8 × 5 = 40. Or find 7 × 5 and add 5.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
8 rows of 5 dots = 40 dots. - A13
A student answers the following question with “64”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: An array has 9 rows, with 7 objects in each row. Split it into smaller arrays and find the total. (3 points)
Reveal explanation
Answer: 63
The suggested answer is not correct. 9 groups of 7 make 9 × 7 = 63. Or find 8 × 7 and add 7.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
9 rows of 7 dots = 63 dots. - A14
Find 7 groups of 8. Can you use 6 groups plus one more? (2 points)
Reveal explanation
Answer: 56
7 groups of 8 make 7 × 8 = 56. Or find 6 × 8 and add 8.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
7 rows of 8 dots = 56 dots. - A15
81 counters are shared equally into 9 groups. How many counters are in each group? (2 points)
Reveal explanation
Answer: 9
Use inverse multiplication: 9 × 9 = 81; therefore 81 ÷ 9 = 9.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
9 rows of 9 dots = 81 dots. - A16
Find 9 groups of 7. Can you use 8 groups plus one more? (2 points)
Reveal explanation
Answer: 63
9 groups of 7 make 9 × 7 = 63. Or find 8 × 7 and add 7.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
9 rows of 7 dots = 63 dots. - A17
A student answers the following question with “36”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: An array has 7 rows, with 5 objects in each row. Split it into smaller arrays and find the total. (3 points)
Reveal explanation
Answer: 35
The suggested answer is not correct. 7 groups of 5 make 7 × 5 = 35. Or find 6 × 5 and add 5.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
7 rows of 5 dots = 35 dots. - A18
Use two useful multiplication facts to work out 8 × 8. What is the product? (2 points)
Reveal explanation
Answer: 64
8 groups of 8 make 8 × 8 = 64. Or find 7 × 8 and add 8.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
8 rows of 8 dots = 64 dots. - A19
Explain how splitting 9 equal groups of 8 helps you find their total. (2 points)
Reveal explanation
Answer: 72
9 groups of 8 make 9 × 8 = 72. Or find 8 × 8 and add 8.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
9 rows of 8 dots = 72 dots. - A20
Use two useful multiplication facts to work out 7 × 8. What is the product? (2 points)
Reveal explanation
Answer: 56
7 groups of 8 make 7 × 8 = 56. Or find 6 × 8 and add 8.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
7 rows of 8 dots = 56 dots. - A21
A student answers the following question with “11”. Explain whether the answer is correct, then solve the question and justify your answer. Original question: Each tray holds 8 counters. How many full trays are required to arrange 80 counters? (3 points)
Reveal explanation
Answer: 10
The suggested answer is not correct. Find how many groups of 8 fit into 80: 80 ÷ 8 = 10.
Scoring: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.
8 rows of 10 dots = 80 dots. - A22
Find 6 groups of 9. Can you use 5 groups plus one more? (2 points)
Reveal explanation
Answer: 54
6 groups of 9 make 6 × 9 = 54. Or find 5 × 9 and add 9.
Scoring: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.
6 rows of 9 dots = 54 dots. - A23
An array has 7 rows of 3 dots. A student says turning it creates 3 more dots. Explain the error and find the total. (3 points)
Reveal explanation
Answer: 21
Turning an array swaps rows and columns but adds no dots. Both 7 × 3 and 3 × 7 equal 21.
Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.
- A24
Without counting individual counters, show two different decompositions for 6 × 4, and explain why both work. (3 points)
Reveal explanation
Answer: 24
One decomposition is (5 × 4) + (1 × 4) = 24. Another is (3 × 4) + (3 × 4) = 24. The partitions use different group splits but preserve the same product.
Scoring: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.